June 2025 | Oceanography
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bathymetric features (e.g., Bell, 1975). They differ from near-
inertial IGWs that are generated by high-frequency wind forc
ing that have frequencies near the Coriolis frequency (Pollard
and Millard, 1970). Aside from internal tides and near-inertial
waves, there is a spread of internal wave energy known as the
IGW continuum spectrum (Garrett and Munk, 1975), which
can be shaped by mesoscale eddies (Barkan et al., 2017) and
nonlinear interactions. Nonlinear interactions can bring IGW
scales down to 1 m or less and can cause IGWs to overturn and
break, a dominant process in the mixing of the ocean interior
(MacKinnon et al., 2017).
IGWs can be discussed in terms of their vertical structures, or
“modes” (Gill, 1982). These modes approximate IGW dynamics
as a linear superposition of standing waves in the vertical direc
tion and propagating waves in the horizontal direction. This is
reasonable in a buoyancy-driven flow where the horizontal scale
is much greater than that of the vertical. Each wave mode has
a characteristic length, phase speed, and vertical structure that
depends on the frequency of the IGW, the Coriolis frequency,
and the vertical density gradient. The lowest baroclinic mode
has a singular, two-layer horizontal structure (i.e., the veloci
ties are out of phase above and below the thermocline); higher
modes have greater vertical structure. Waves in the IGW spec
trum at frequencies greater than tidal frequency, called super
tidal, are thought to arise from nonlinear interactions between
internal tides and near-inertial IGWs (Müller et al., 1986).
IGW variability has not been well captured by global ocean
simulations. Simulations may lack certain forcing (e.g., tidal)
or may parameterize, rather than resolve, finer-scale processes.
Barotropic tidal models, where water movement is uniform with
depth, have been available since the 1970s (e.g., Hendershott,
1981), but they do not allow stratified flow. In the last two
decades, increases in computational power have made it possi
ble to accurately model internal tides in a stratified ocean. These
models have evolved from using horizontally uniform two-layer
(Arbic et al., 2004) or multilayer (Simmons et al., 2004) stratifi
cation to embedding tidal forcing in ocean general circulation
simulations with stratification that varies geographically in a
realistic manner (Arbic et al., 2012).
This study focused on the modeling of internal tides and
IGWs in HYCOM, the backbone of the operational forecasting
system of the US Navy (Metzger et al., 2014). The Navy HYCOM
simulations use a hybrid vertical coordinate system: isopycnal
coordinates in the stratified ocean interior, a dynamic transi
tion to pressure (p) coordinates in the surface mixed layer, and
bathymetry-following (σ) coordinates in shallow shelf water
(Bleck, 2002; Chassignet et al., 2006). The simulations use real
istic atmospheric forcing from the Navy Global Environmental
Model (NAVGEM; Hogan et al., 2014) and can be run with or
without data assimilation and with or without tidal forcing.
Sophisticated methods from the data-assimilation literature
have also been applied to bring the tidal simulations closer to
observations (Ngodock et al., 2016).
For this study, HYCOM was primarily utilized without data
assimilation. Data assimilation can create “shocks” as it brings
the model closer to observations, disrupting the geostrophic
balance between horizontal pressure gradients and rotation.
Raja et al. (2024) found that as the modeled ocean tries to restore
geostrophic balance, spurious low-mode internal waves are gen
erated. These waves have frequencies that overlap with the tidal
and inertial bands, complicating the analysis of naturally occur
ring tidal and near-inertial waves. The interaction of these spuri
ous IGWs with other internal waves or eddies and their eventual
dissipation can also alter the ocean energetics. For this reason,
most of our HYCOM internal tide and IGW studies (e.g., Raja
et al., 2022), and subsequent acoustics research for this project,
have used HYCOM simulations without data assimilation.
The HYCOM model was used in this study with a variety of
vertical, horizontal, and bathymetric grid spacings. The most-
used model setups were regional and global versions of tidally
forced HYCOM with a horizontal grid spacing of 1/25° to 1/50°,
typically the highest resolution spacing at which Global HYCOM
can be run. This is finer than the 1/12° grid spacing available in
most of today’s publicly available global ocean models. Idealized
versions of the model, such as using a single temperature-
salinity profile in a two-dimensional field, were used to isolate
the effects of internal tides on stratification and energy trans
fer. Regional simulations using the Massachusetts Institute of
Technology general circulation model (MITgcm) were com
pared to HYCOM simulations because of MITgcm’s different
boundary conditions and, for this study, its finer grid spacing.
Sound Propagation
Internal tides and IGWs have long been associated with under
water acoustics. The influence of internal tides and IGWs on
sound speed variability has been at the core of many observa
tional (e.g., Flatté et al., 1979; Tang et al. 2007; Worcester et al.,
2013) and modeling (e.g., Colosi and Flatté, 1996) studies.
Alternatively, acoustic tomography, an inverse method that uses
long-range acoustic propagations to infer ocean structure, has
been used to study the barotropic and baroclinic tides themselves
(Dushaw, 2022). In addition to the tilt of density surfaces caused
by internal waves, temperature and salinity fluctuations along a
constant density surface, called “spice,” can have a similarly large
impact on sound speed and its gradients (Dzieciuch et al., 2004).
“Spiciness,” caused by ocean stirring by mesoscale eddies, could
differ between tidal and non-tidally forced ocean simulations.
This study focused on upper ocean acoustic structure and
propagation. In the uniform temperature and salinity layer found
at the ocean surface in many regions, pressure causes sound
speed to increase with depth, often creating a local subsurface
maximum in sound speed (Helber et al., 2008). This subsur
face sound-speed maximum, called the sonic layer depth (SLD),
has the potential to form a surface-layer duct where sound is